Using the same power source for microcontroller (arduino) and rest of the circuit?

I have an Arduino, it controls a 6V DC motor and 12V DC solenoid (which only really needs 7V for what its doing).

Originally I wanted to use 1 rechargeable 7V battery (or 9 or whatever the closest I can get) to power all three of these.

But I've been seeing recommendations from people to use separate power supplies for Arduino and the rest of the circuit, otherwise they describe a lot of "noise" when the motor and solenoid suddenly engage. (not sure what is meant by "noise")

So is there a way to accomplish my task with one 7 - 12V power supply??